Those oil pressure numbers are not up to spec for a freshly rebuilt 8BA. In my experience, it should idle around 25-35 psi and run at over 50, hot or cold. Do you know what kind of oil pump was installed? I tried to save a few bucks on my latest build and installed a standard Speedway Motors oil pump. I think it is causing me problems with this engine.
The oil pressure on this engine is not where I expect it to be. It idles cold at 20, but goes right up to over 50 when I rev it up. At hot idle, it drops to 10 psi. I know a lot of you guys are OK with that and quote the old "10 lbs per 1000 rpm" saw, but in my opinion, this is not correct for a fresh rebuild. I have a correct tested Ford pump I am going to install in the next couple of days. I expect it to make a difference and bring my oil pressure back to where it should be. The way the oil pressure reacts to engine speed, I expect the spring is too "soft" on the low end and opens partially at low RPM. When engine speed comes up, the additional volume produced by the pump can't go through the partially open relief and the pressure increases. I will post what I find when I have the Ford pump installed.
Upon re-reading your last post. it looks like you are experiencing oil pressure numbers that are very similar to mine. Did you, perchance, have a Speedway oil pump installed?